Question

roblem 1. [3.0p] Let u AD, DC, - CB and dicates. Assume that ABCD is a parallelogram with AD parallel to BC. BA, as the figure Explain why AD-BC a. b. Explain why c. Write AC in terms of ü and e. d. Write AC in terms of z and u e. Find the sums i+a, ( +u ) + 6 , and ( (z +a) +6 ) + 0 , and express the anstwers in terms of the vertices of the parallelogram. f. Show geometrically that vector addition is associative; that is, (u+e)+ w) -+ ( + @) [Hints: Use the triangular rule for addition Figure 0.1: Parallelogram

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Answer 1

(b) fnee the CA DC vector clireatfon fe dliffenent +he beut (opporite) Hence See thort From 4he C CEn We AC AD 1 tvfangulan f delolitfon from rule AC + d) fiaune From the hat gee can we (triangulan 7de of adlolftfon) CP +BA CA - AC R AC

(a) ince Prpan oeor hat TC CInd AD is panillel to inyomel Proof paralle log ancl D Bt η Opposfte ραταlle TOm g Pdes ef Stnce, ADIIDL .and AC Trcins vensal LOCA AItenneute fatestor anle) a nd &AC P transvensal ADI1 LOCA CAItennet e Pntenior AA BC Now, in q nd A A Dc LOAC LBCA Cincl LAAC -LDCA AC Ps C ommon gimilanity A ABC Fiom AS A 4ADC provedd Hence AD= BC olfrectfon AD , BC ard thene as AD = Same

(e) From 4he fi thas tve can see law of adotition A + AD =- ) h and A0 0- 0 +0--& 1 ngain an -t mt be proved can also It ides of all vectoial ctose of 6ome Ts zero (.

K4C From fig A (nw ef adolon + (LH) AC (a+0 1 and AC BA AC - R -> Ac - n (a w a gtotifion again Now DA a nel AB AD (RHS) a 8) 0 440) Hente Proveat LHS RHS